The present invention relates to a method of estimating the frequency offset of a packet of phase-modulated symbols that have been received with phase error.
The invention relates to demodulating signals that have been modulated by phase shift keying (PSK), and more particularly to estimating the frequency and phase offsets that are necessary for demodulating signals in packet form that have been modulated by phase modulation, or by phase-and-amplitude modulation. The invention applies to the field of transmission, for the purpose of demodulating digital signals transmitted in the form of packets. A typical digital transmission channel comprises a binary source, an encoder, a modulator which transmits into the channel, a demodulator at the outlet from the channel, and a decoder which delivers the binary signal. Channel encoding is used to reduce the power needed to achieve a given bit error rate. Modulation and demodulation enable transmission to be performed over the selected channel. Insofar as the invention relates to demodulation, the other elements of the transmission system, such as source encoding and decoding are not described in greater detail.
M. Morelli and U. Mengali, xe2x80x9cFeedforward frequency estimation for PSK: a tutorial reviewxe2x80x9d, ETT Vol. 9, No. 2, March-April 1998, contains a description of the problem of synchronization in demodulators for digital transmission systems using phase modulation in packet mode. That document also describes the known solutions to the problem.
The problem of demodulating phase modulated digital signals that have been transmitted in packet mode arises particularly in satellite transmission systems using time division multiple access (TDMA), or for land cellular telecommunications systems. This is a major technical problem in the field of telecommunications.
More precisely, the invention provides a method of estimating the frequency offset of a packet of phase-modulated symbols that has been received with phase error, the method comprising:
applying a phase correction to the symbols of the received packet for all possible pairs of frequency offset and phase offset; and
selecting from said offset pairs, the pair which provides the most likely packet of corrected symbols, thereby determining the frequency offset of the received packet.
In an implementation, the method further includes a step of quantizing possible phase corrections.
Preferably, the selection step comprises:
calculating a metric between the packet of symbols as received and phase-corrected and an estimate of the packet of symbols as sent; and
seeking a minimum value of said metric.
In another implementation, the packet of symbols sent is estimated:
for known symbols, by using the transmitted symbol; and
for unknown symbols, by taking a firm decision.
Advantageously, rotation through ej2xcfx80/k, where k is a natural integer, leaves the set of possible symbols invariant, and possible phase values are selected from a range of [0, 2xcfx80/k].
In another implementation, the phase correction applied to the symbols, for a frequency offset value fm and for a phase offset value xcfx86k is written exe2x88x92j(2xcfx80fm(pxe2x88x921)Ts+xcfx86k), where p is the position of the symbol and Ts is the symbol time.
In this case, the values of the argument xe2x88x92(2xcfx80fm(pxe2x88x921)Ts+xcfx86k) are preferably calculated in the form of reduced values, e.g. over a range [0, 2xcfx80].
The method can further comprise a prior step of calculating and storing all possible phase corrections to be applied to a symbol.
The method can further comprise a step of estimating the phase offset as being the phase offset value in said pair that provides the most likely packet of corrected symbols.